**Introduction.** In Bologna Process half of teaching time is dedicated for independent activity of the students. Computer support of the educational process provides wide opportunities for independent work of students and their work in classrooms. Therefore, virtual learning environment platform (VLE) could be an essential tool for solving the task of increasing the quality of education. In spite of the problem of educational knowledge and information accessing in e-learning is successfully resolved, the online testing and assessment remains a relevant scientific and methodical issue that requires a solution. Lviv Polytechnic National University Institutional Repository http://ena.lp.edu.ua 36 Testing of students in mathematics. Main attention is paid to checking the skills and abilities in defining the level of training of students in mathematics. The main type of questions in this case requires answer as a formula. Closed-forms of questions do not involve checking of a number of tasks [1,2]. In the open type questions there is a problem of ambiguity forms of answers, all of which are correct. It is quite easy to modify most of the open source learning management systems and WYSIWYG formula editors [3]. It can be easily done by the implementation of research projects in the institutions to engage students with relevant programming skills. Proposed modification of the formula editor provides the creation of templates for entering formulas and indexing algorithm using elements of expression that allows to avoid ambiguity during online student testing. The tasks with computer verifying of analytical symbolic expression can be applied for automation of skills and knowledge checking in natural sciences by appropriate modification of the template [4].

**The main steps of algorithm.** The main steps of the data verification algorithm are to perform the indexing of array elements in groups, checking commutative, associative and distributive operations. The proposed algorithm provides formalization of entered answer, and represents elements of the formula expression in a structured, suitable for computer processing form. Further processing provides comparison with the reference value using a probabilistic approach to assessing students’ knowledge.** **

**Adaptive student learning. **Also this model is convenient for adaptive student learning. Questions with the wrong student’s answer recorded in a database for subsequent testing. After working through the theoretical material of these issues (along with other issues from question bank problems in an appropriate ratio, given by the teacher) students perform re-examination. Question is removed from the database after correct answer. The number of possible tests depends on an assessment of the previous test.

**Conclusions.** Сomputer based testing is widely used to evaluate students’ knowledge during selftesting and quizzes. Principles of knowledge examination of mathematical subject testing in e-learning environments have been developed. Component analysis and formula expression indexing algorithm for automatic analysis is suggested. Due to the proposed algorithm it is much more easier to verificate a large number of mathematical solution examples with a large number of students. This approach allows to diversify the types of questions for consequent verification and implementation in computer systems.

1. AVANESOV, V. (1994) Scientific problems of test knowledge control. – Moscow: Research center (in Russian).

2. ZHARKIH, YU., LYSOCHENKO, S., SUS, B. and TRETYAK, O. (2012) Computer Technologies in Education. – Kyiv. Taras Shevchenko University (in Ukrainian).

3. FIREMATH. (2013) – The MathML Editor. [Electronic Resource]. – Available from: http://www.firemath.info/ – Title from the screen. [Accessed: 19th November 2013].

4. TMYENOVA N.P., SUSE B.B. (2013) Features of computer mathematics testing in e-learning environments // 5th Scientific Conference Preceedings “Innovative computer technologies in higher education”, Tuesday 19th to Thursday 21st November 2013. NULP Lviv (Ukraine), рр. 52-55.